Two-dimensional isometric tensor networks on an infinite strip

Journal Article · 08 June 2023 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.107.245118 · OSTI ID:2234108

Wu, Yantao  ^[1]; Anand, Sajant  ^[2]; Lin, Sheng-Hsuan  ^[3]; Pollmann, Frank ^[3]; Zaletel, Michael P. ^[4]

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1. Inst. of Physical and Chemical Research (RIKEN), Wako (Japan). Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS); Univ. of California, Berkeley, CA (United States)
2. Univ. of California, Berkeley, CA (United States)
3. Technische Univ., Munich (Germany)
4. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

The exact contraction of a generic two-dimensional (2D) tensor network state (TNS) is known to be exponentially hard, making simulation of 2D systems difficult. The recently introduced class of isometric TNS (isoTNS) represents a subset of TNS that allows for efficient simulation of such systems on finite square lattices. The isoTNS ansatz requires the identification of an “orthogonality column” of tensors, within which one-dimensional matrix product state (MPS) methods can be used for calculation of observables and optimization of tensors. Here we extend isoTNS to infinitely long strip geometries and introduce an infinite version of the Moses Move algorithm for moving the orthogonality column around the network. Using this algorithm, we iteratively transform an infinite MPS representation of a 2D quantum state into a strip isoTNS and investigate the entanglement properties of the resulting state. In addition, we demonstrate that the local observables can be evaluated efficiently. Finally, we introduce an infinite time-evolving block decimation algorithm (iTEBD²) and use it to approximate the ground state of the 2D transverse field Ising model on lattices of infinite strip geometry.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF)
• Grant/Contract Number: AC02-05CH11231; SC0022716
• OSTI ID: 2234108
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 24 Vol. 107; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English